Solving Integer Linear Programs with a Small Number of Global
Variables		and Constraints

D 2017

Solving Integer Linear Programs with a Small Number of Global Variables and Constraints

DVORAK, Pavel, Eduard EIBEN, Robert GANIAN, Dusan KNOP, Sebastian ORDYNIAK et. al.

Basic information

Original name

Solving Integer Linear Programs with a Small Number of Global Variables and Constraints

Authors

DVORAK, Pavel (203 Czech Republic), Eduard EIBEN (703 Slovakia), Robert GANIAN (203 Czech Republic, guarantor, belonging to the institution), Dusan KNOP (203 Czech Republic) and Sebastian ORDYNIAK (40 Austria)

Edition

USA, Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence, {IJCAI} 2017, Melbourne, Australia, August 19-25, 2017, p. 607-613, 7 pp. 2017

Publisher

ijcai.org

Other information

Language

English

Type of outcome

Stať ve sborníku

Field of Study

10200 1.2 Computer and information sciences

Country of publisher

United States of America

Confidentiality degree

není předmětem státního či obchodního tajemství

Publication form

electronic version available online

References:

URL

RIV identification code

RIV/00216224:14330/17:00100548

Organization unit

Faculty of Informatics

ISBN

978-0-9992411-0-3

ISSN

DOI

http://dx.doi.org/10.24963/ijcai.2017/85

UT WoS

000764137500085

Keywords in English

Integer Linear Programming; Backdoors; Parameterized Algorithms

Abstract

V originále

Integer Linear Programming (ILP) has a broad range of applications in various areas of artificial intelligence. Yet in spite of recent advances, we still lack a thorough understanding of which structural restrictions make ILP tractable. Here we study ILP instances consisting of a small number of ``global'' variables and/or constraints such that the remaining part of the instance consists of small and otherwise independent components; this is captured in terms of a structural measure we call fracture backdoors which generalizes, for instance, the well-studied class of N-fold ILP instances. Our main contributions can be divided into three parts. First, we formally develop fracture backdoors and obtain exact and approximation algorithms for computing these. Second, we exploit these backdoors to develop several new parameterized algorithms for ILP; the performance of these algorithms will naturally scale based on the number of global variables or constraints in the instance. Finally, we complement the developed algorithms with matching lower bounds. Altogether, our results paint a near-complete complexity landscape of ILP with respect to fracture backdoors.

Citovat

DVORAK, Pavel, Eduard EIBEN, Robert GANIAN, Dusan KNOP and Sebastian ORDYNIAK. Solving Integer Linear Programs with a Small Number of Global Variables and Constraints. Online. In Carles Sierra. Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence, {IJCAI} 2017, Melbourne, Australia, August 19-25, 2017. USA: ijcai.org, 2017, p. 607-613. ISBN 978-0-9992411-0-3. Available from: https://dx.doi.org/10.24963/ijcai.2017/85.

@inproceedings{1414040,
   author = {Dvorak, Pavel and Eiben, Eduard and Ganian, Robert and Knop, Dusan and Ordyniak, Sebastian},
   address = {USA},
   booktitle = {Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence, {IJCAI} 2017, Melbourne, Australia, August 19-25, 2017},
   doi = {http://dx.doi.org/10.24963/ijcai.2017/85},
   editor = {Carles Sierra},
   keywords = {Integer Linear Programming; Backdoors; Parameterized Algorithms},
   howpublished = {elektronická verze "online"},
   language = {eng},
   location = {USA},
   isbn = {978-0-9992411-0-3},
   pages = {607-613},
   publisher = {ijcai.org},
   title = {Solving Integer Linear Programs with a Small Number of Global Variables and Constraints},
   url = {https://www.ijcai.org/proceedings/2017/85},
   year = {2017}
}

TY  - JOUR
ID  - 1414040
AU  - Dvorak, Pavel - Eiben, Eduard - Ganian, Robert - Knop, Dusan - Ordyniak, Sebastian
PY  - 2017
TI  - Solving Integer Linear Programs with a Small Number of Global Variables and Constraints
PB  - ijcai.org
CY  - USA
SN  - 9780999241103
KW  - Integer Linear Programming
KW  - Backdoors
KW  - Parameterized Algorithms
UR  - https://www.ijcai.org/proceedings/2017/85
L2  - https://www.ijcai.org/proceedings/2017/85
N2  - Integer Linear Programming (ILP) has a broad range of applications in various areas of artificial intelligence. Yet in spite of recent advances, we still lack a thorough understanding of which structural restrictions make ILP tractable. Here we study ILP instances consisting of a small number of ``global'' variables and/or constraints such that the remaining part of the instance consists of small and otherwise independent components; this is captured in terms of a structural measure we call fracture backdoors which generalizes, for instance, the well-studied class of N-fold ILP instances. Our main contributions can be divided into three parts. First, we formally develop fracture backdoors and obtain exact and approximation algorithms for computing these. Second, we exploit these backdoors to develop several new parameterized algorithms for ILP; the performance of these algorithms will naturally scale based on the number of global variables or constraints in the instance. Finally, we complement the developed algorithms with matching lower bounds. Altogether, our results paint a near-complete complexity landscape of ILP with respect to fracture backdoors.
ER  -

DVORAK, Pavel, Eduard EIBEN, Robert GANIAN, Dusan KNOP and Sebastian ORDYNIAK. Solving Integer Linear Programs with a Small Number of Global Variables and Constraints. Online. In Carles Sierra. \textit{Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence, $\{$IJCAI$\}$ 2017, Melbourne, Australia, August 19-25, 2017}. USA: ijcai.org, 2017, p.~607-613. ISBN~978-0-9992411-0-3. Available from: https://dx.doi.org/10.24963/ijcai.2017/85.

Detailed Information on Publication Record